Inequality of Bogomolov-Gieseker's type on arithmetic surfaces
alg-geom
2008-02-03 v1 Algebraic Geometry
Abstract
Let K be an algebraic number field, O_K the ring of integers of K, and f : X --> Spec(O_K) an arithmetic surface. Let (E, h) be a rank r Hermitian vector bundle on X such that is semistable on the geometric generic fiber of f. In this paper, we will prove an arithmetic analogy of Bogomolov-Gieseker's inequality: c_2(E, h) - (r-1)/(2r) c_1(E, h)^2 >= 0.
Keywords
Cite
@article{arxiv.alg-geom/9305005,
title = {Inequality of Bogomolov-Gieseker's type on arithmetic surfaces},
author = {Atsushi Moriwaki},
journal= {arXiv preprint arXiv:alg-geom/9305005},
year = {2008}
}
Comments
51 pages, AmSTeX